According to Good Housekeeping, it is safe to eat sprouting potatoes if the sprouts are cut away and not consumed. In addition, any green parts of the potato should be removed before the potato is eaten.
MedlinePlus, a service of the U.S. National Library of Medicine, specifically warns against eating potato sprouts or green potatoes because it can result in potato poisoning. Sprouts and green potatoes contain solanine, which is toxic. This chemical is dangerous even when small amounts are ingested. Symptoms of potato poisoning include, but are not limited to, vomiting, diarrhea, hallucinations, low body temperature and headache. According to MedlinePlus, medical personnel should be consulted if potato poisoning is suspected.